# mixgamma: Mixture of Gamma distribution In bmixture: Bayesian Estimation for Finite Mixture of Distributions

## Description

Random generation and density function for the finite mixture of Gamma distribution.

## Usage

 1 2 3 rmixgamma( n = 10, weight = 1, alpha = 1, beta = 1 ) dmixgamma( x, weight = 1, alpha = 1, beta = 1 ) 

## Arguments

 n  The number of samples required. x  The vector of quantiles. weight The vector of probability weights, with length equal to number of components (k). This is assumed to sum to 1; if not, it is normalized. alpha  The vector of non-negative parameters of the Gamma distribution. beta  The vector of non-negative parameters of the Gamma distribution.

## Details

Sampling from finite mixture of Gamma distribution, with density:

Pr(x|\underline{w}, \underline{α}, \underline{β}) = ∑_{i=1}^{k} w_{i} Gamma(x|α_{i}, β_{i}),

where

Gamma(x|α_{i}, β_{i})=\frac{(β_{i})^{α_{i}}}{Γ(α_{i})} x^{α_{i}-1} e^{-β_{i}x}.

## Value

Generated data as an vector with size n.

## References

Mohammadi, A., Salehi-Rad, M. R., and Wit, E. C. (2013) Using mixture of Gamma distributions for Bayesian analysis in an M/G/1 queue with optional second service. Computational Statistics, 28(2):683-700

Mohammadi, A., and Salehi-Rad, M. R. (2012) Bayesian inference and prediction in an M/G/1 with optional second service. Communications in Statistics-Simulation and Computation, 41(3):419-435

rmixnorm, rmixt

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ## Not run: n = 10000 weight = c( 0.6 , 0.3 , 0.1 ) alpha = c( 100 , 200 , 300 ) beta = c( 100/3, 200/4, 300/5 ) data = rmixgamma( n = n, weight = weight, alpha = alpha, beta = beta ) hist( data, prob = TRUE, nclass = 30, col = "gray" ) x = seq( -20, 20, 0.05 ) densmixgamma = dmixnorm( x, weight, alpha, beta ) lines( x, densmixgamma, lwd = 2 ) ## End(Not run) 

### Example output

Loading required package: BDgraph

Attaching package: 'igraph'

The following objects are masked from 'package:stats':

decompose, spectrum

The following object is masked from 'package:base':

union

Attaching package: 'BDgraph'

The following object is masked from 'package:igraph':

compare


bmixture documentation built on Sept. 11, 2019, 9:07 a.m.